{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Original paper by Kronig, Penney:\n",
    "\n",
    "R. de L. Kronig, W.G.Penney, Proc. Roy. Soc. (London) A130, 499 (1931)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "import matplotlib.pylab as plt\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve an entire system of multiple wells\n",
    "The technique heres appears to be a finite difference type method, i.e. approximate the second derivative in the 1D Schrodinger's equation with 2nd order accurate finite differences (central difference scheme). Then just diagonalize the matrix (this is what they call \"exact diagonalization\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-100. -100. -100. -100.    0.    0.    0.    0.    0.    0. -100. -100.\n",
      " -100. -100.    0.    0.    0.    0.    0.    0. -100. -100. -100. -100.\n",
      "    0.    0.    0.    0.    0.    0. -100. -100. -100. -100.    0.    0.\n",
      "    0.    0.    0.    0. -100. -100. -100. -100.    0.    0.    0.    0.\n",
      "    0.    0. -100. -100. -100. -100.    0.    0.    0.    0.    0.    0.\n",
      " -100. -100. -100. -100.    0.    0.    0.    0.    0.    0. -100. -100.\n",
      " -100. -100.    0.    0.    0.    0.    0.    0. -100. -100. -100. -100.\n",
      "    0.    0.    0.    0.    0.    0. -100. -100. -100. -100.    0.    0.\n",
      "    0.    0.    0.    0. -100. -100. -100. -100.    0.    0.    0.    0.\n",
      "    0.    0. -100. -100. -100. -100.    0.    0.    0.    0.    0.    0.\n",
      " -100. -100. -100. -100.    0.    0.    0.    0.    0.    0. -100. -100.\n",
      " -100. -100.    0.    0.    0.    0.    0.    0. -100. -100. -100. -100.\n",
      "    0.    0.    0.    0.    0.    0. -100. -100. -100. -100.    0.    0.\n",
      "    0.    0.    0.    0. -100. -100. -100. -100.    0.    0.    0.    0.\n",
      "    0.    0. -100. -100. -100. -100.    0.    0.    0.    0.    0.    0.\n",
      " -100. -100. -100. -100.    0.    0.    0.    0.    0.    0. -100. -100.\n",
      " -100. -100.    0.    0.    0.    0.    0.    0.]\n"
     ]
    }
   ],
   "source": [
    "n_potentials = 20\n",
    "dx = 0.1\n",
    "steps_per_well = np.int(1. / dx)\n",
    "potential_width = np.int(0.4 / dx)\n",
    "n_x = np.int(n_potentials / dx)\n",
    "V_0 = -100\n",
    "\n",
    "V = np.zeros(n_x)\n",
    "\n",
    "for i in range(n_potentials):\n",
    "    left = i * steps_per_well\n",
    "    right = i * steps_per_well + potential_width\n",
    "    V[left:right] = V_0\n",
    "print(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21dfd0f62e8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "H = np.zeros((n_x, n_x))\n",
    "np.fill_diagonal(H, 2 * 1 + dx * dx * V)\n",
    "H = H + np.diag(-1 * np.ones(n_x - 1), -1) \n",
    "H = H + np.diag(-1 * np.ones(n_x - 1), +1) \n",
    "\n",
    "H[0, -1] = -1\n",
    "H[-1, 0] = -1\n",
    "plt.imshow(H);\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "evals, evecs = la.eigh(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21dfcf6fb70>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(evecs[:, 2], color=\"red\", linewidth=3, zorder=10)\n",
    "ax_t = plt.twinx()\n",
    "ax_t.plot(V, color=\"grey\")\n",
    "ax_t.set_ylim([V_0 * 1.1, np.abs(V_0)/10])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Determination of the Bloch factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "dx = 0.01\n",
    "steps_per_well = np.int(1. / dx)\n",
    "potential_width = np.int(0.4 / dx)\n",
    "n_x = 20\n",
    "\n",
    "V_0 = 30\n",
    "V = np.zeros(steps_per_well)\n",
    "n_w = steps_per_well\n",
    "B = np.zeros((n_w, n_w), dtype=np.complex)\n",
    "ks = 1.j * np.linspace(-np.pi, np.pi, n_x)\n",
    "\n",
    "for i in range(1):\n",
    "    left = i * steps_per_well\n",
    "    right = i * steps_per_well + potential_width\n",
    "    V[left:right] = V_0\n",
    "\n",
    "bnd_0 = []\n",
    "bnd_1 = []\n",
    "bnd_2 = []\n",
    "bnd_3 = []\n",
    "\n",
    "for k in ks:\n",
    "    B[:] = 0. + 0.j\n",
    "    \n",
    "    np.fill_diagonal(B, +2 * 1 + dx * dx * (np.abs(k * k) + V))\n",
    "    B = B + np.diag((-1 + k * dx) * np.ones(n_w - 1), -1)\n",
    "    B = B + np.diag((-1 - k * dx) * np.ones(n_w - 1), +1)\n",
    "\n",
    "    # periodic boundary conditions\n",
    "    B[0, -1] = -1 + k * dx\n",
    "    B[-1, 0] = -1 - k * dx\n",
    "    \n",
    "    evals, evecs = la.eigh(B)\n",
    "    bnd_0.append(evals[0] / (dx * dx))\n",
    "    bnd_1.append(evals[1] / (dx * dx))    \n",
    "    bnd_2.append(evals[2] / (dx * dx))    \n",
    "    bnd_3.append(evals[2] / (dx * dx))    \n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21dfaabb208>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(bnd_0)\n",
    "plt.plot(bnd_1)\n",
    "plt.plot(bnd_2)\n",
    "plt.plot(bnd_3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21dfe546d68>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.real(evecs[:, 4]))\n",
    "plt.plot(V / 1000)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wannier functions from Kronig Penney functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solve for the Bloch factors**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "V_0 = 100\n",
    "n_unit_cells = 20\n",
    "a = 2.\n",
    "dx = 0.1\n",
    "steps_per_well = np.int(a / dx)\n",
    "potential_width = np.int(0.2 / dx)\n",
    "\n",
    "n_w = steps_per_well\n",
    "V = np.zeros(steps_per_well)\n",
    "B = np.zeros((n_w, n_w), dtype=np.complex)\n",
    "ks = np.array([1.j * (-np.pi / a + 2 * np.pi / a / n_unit_cells * s) for s in range(n_unit_cells)])\n",
    "\n",
    "boundary = np.int(potential_width / 2)\n",
    "boundary = 2\n",
    "V[0:boundary] = V_0\n",
    "V[-boundary:] = V_0\n",
    "\n",
    "evls = {}\n",
    "evcs = {}\n",
    "\n",
    "for nk, k in enumerate(ks):\n",
    "    B[:] = 0. + 0.j\n",
    "    \n",
    "    np.fill_diagonal(B, 2 * 1 + dx * dx * (np.abs(k * k) + V))\n",
    "    B = B + np.diag((-1 + k * dx) * np.ones(n_w - 1), -1)\n",
    "    B = B + np.diag((-1 - k * dx) * np.ones(n_w - 1), +1)\n",
    "\n",
    "    B[0, -1] = -1 + k * dx\n",
    "    B[-1, 0] = -1 - k * dx\n",
    "    \n",
    "    evals, evecs = la.eigh(B)\n",
    "    evls[nk] = evals / (dx * dx)\n",
    "    evcs[nk] = evecs[:, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Build Bloch functions from Bloch factors**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_ungauged = np.zeros((n_unit_cells, n_unit_cells * steps_per_well), dtype=np.complex)\n",
    "\n",
    "for nk in range(n_unit_cells):\n",
    "    for nx in range(n_unit_cells):\n",
    "        for i in range(steps_per_well):\n",
    "            jx = nx * steps_per_well + i\n",
    "            x = jx * dx\n",
    "            psi_ungauged[nk, jx] = np.exp(ks[nk] * x) * evcs[nk][i] / np.sqrt(n_unit_cells)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Gauge Bloch functions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "phases = np.zeros(n_unit_cells, dtype=np.complex)\n",
    "for nk in range(n_unit_cells):\n",
    "    phases[nk] = psi_ungauged[nk, 0] / np.abs(psi_ungauged[nk, 0])\n",
    "    \n",
    "psi_gauged = np.zeros((n_unit_cells, n_unit_cells * steps_per_well), dtype=np.complex)\n",
    "\n",
    "for nk in range(n_unit_cells):\n",
    "    psi_gauged[nk, :] = psi_ungauged[nk, :] / phases[nk]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " **Show the result**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21dfd0081d0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "wannier = np.zeros(n_unit_cells * steps_per_well, dtype=np.complex)\n",
    "i = 1\n",
    "\n",
    "for jx in range(n_unit_cells * steps_per_well):\n",
    "    for nk in range(n_unit_cells):\n",
    "        wannier[jx] += np.exp(-ks[nk] * a * 10) * psi_gauged[nk, jx] / np.sqrt(n_unit_cells)\n",
    "        \n",
    "plt.plot(dx * np.arange(n_unit_cells * steps_per_well), np.real(wannier), color=\"grey\")    \n",
    "plt.axvline(x=i * steps_per_well, linewidth=3)\n",
    "plt.axvline(x=(i + 1) * steps_per_well, linewidth=3)\n",
    "# plt.xlim([10, 30])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
